Jerricho,
I heard that one recently too.
VdeV
I've had the same (limited!) experience as Jazzykex, never been asked to fly at a groundspeed. Theoretically you could stall the aeroplane with a 100kt tailwind but still be doing a significant groundspeed! A bit of a far fetched example, but it's the aircraft speed through the air that is important to us, not the groundspeed. For separation purposes of a/c on the same route we are asked to fly at set Mach numbers to keep the required separation. For instance the a/c in front will be asked his Mach and if he replies M.80 then he may be told to maintain Mach.80 minimum and the a/c behind told to fly M.80 maximum. Or at least that's what has always happened to me. For converging traffic at the same level I have either been given a vector or instructed to climb/ descend to ensure separation. So far never asked to fly a groundspeed.
PP